Phys. Med. Biol. 38 (1993) 959-970. Printed in the UK
A neural network approach to automatic chromosome
c1assfication
Anne M Jennings and Jim Graham
Depanment of Medical Biophysics, Universiw of Manchester, UK
Received 5 October 1992, in final form 1 April 1993
Abstract. Classification of banded metaphase chromosomes is an important step io automated
clinical chromosome analysis. We have conducted a preliminary investigation of the application
of aaificial neural networks to this process, making use of a natural representation of the banding
pattern. Two different network architectures have been compared the Kohonen %IF-organizing
feature map and the multi-layer perceptron (MLP). For each of these a search of their respective
parameter spaces over a limited range has resulted in configurations of modest dimension which
achieve creditable classification mes. The MLP in particular shows promise of being a useful
classifier. When size and shape features are supplied as inputs to the MLP in addition to a
low-resolution banding profile, misclassificatinn lates are obtained which are comparable with
those of a well developed statistical classifier.
1. Introduction
In a normal human cell there are 46 chromosomes which, at an appropriate stage of
cell division (metaphase), can be observed as separate objects using high-resolution light
microscopy. Appropriately stained they show a series of bands along their length and a
characteristic constriction called the centromere. Figure l(a) shows a typical metaphase cell,
stained to produce the most commonly used banding appearance (G banding). Chromosome
analysis, which involves visual examination of these cells, is routinely undertaken in hospital
laboratories, for example for pre-natal diagnosis of genetic abnormality or monitoring of
cancer treatment.
This visual analysis involves counting the chromosomes and examining them for
structural abnormalities. To determine the significance of both numerical and structural
abnormality it is necessary to classify the chromosomes into 24 groups on the basis of
their size, the pattern of bands and the centromere position. Twenty two of these groups
normally contain two homologous (structurally identical) chromosomes. The other two
groups contain the sex chromosomes X and Y. In the case of a normal male cell, the X and
Y groups contain one chromosome each; in a female cell there is a homologous pair of X
chromosomes and the Y group is empty.
The time consuming nature of chromosome analysis has resulted in considerable interest
in the development of automated systems based on machine vision. A number of such
systems are now in routine use in many hospitals (see, e.g. Graham 1987, Graham and
Pycock 1987; for a review see Lundsteen and Martin 1989). The chromosome classification
performance of these systems depends on the type of material used, but is at best in the
range 6 1 8 % misclassification (Piper and Granum 1989). This compares poorly with visual
classification by cytotechnician, which was estimated by Lundsteen etal (1976) to result in
0031-9155/93/070959+12$07.50 @ 1993 IOP Publishing Ltd
959
960
A M Jennings and J Graham
Figure 1. Chromosomes and chromosome feahlres. ( a ) A cell at metaphase. The individual
chromosomes show the banding paftem (G banding) produced by staining. ( b ) Schematic
drawing of a chromosome showing the position of the centromere. The density profile (helaw)
is formed by projecting the density onto the curved centreline.
a classification error rate of 3% for inspection of isolated chromosomes, dropping to 0.1%
when all chromosomes in a cell could be examined together. All automated systems in
clinical use operate interactively, allowing an expert operator to correct machine errors in
image segmentation, feature extraction and classification, resulting in useful performance
(Graham and Piper 1993). However, there is clear scope for improvement in automatic
classification.
An important issue for automatic classification is the representation of the banding
pattern. Several different classifiers have been reported using statistical or syntactic
approaches (Granlund 1976, Granum 1982, Lundsteen et al 1981, Groen et al 1989,
Thomason and Granum 1986). Each of these involves the extraction of a number of
intuitively defined features, usually associated with the chromosome’s density profile.
The density profile is a one-dimensional pattern obtained by projecting the chromosome’s
density onto its centre line (figure l(b)),and reflects the largely linear organization of the
chromosome structure.
The processing involved in extracting features from the profiles involves the risk of
losing information, a risk which may he eliminated by using the density profile itself as the
handing representation. This type of one-dimensional pattern is a natural form of input for
artificial neural networks, in which the classification features are selected automatically by
a process of training from examples. Neural networks have been successfully used for a
range of pattern recognition applications (Kohonen 1988, Sejnowski and Rosenburg 1987,
Haykin and Deng 1991). Their advantages lie in their ability to correctly classify noisy or
incomplete data and the relative ease with which they can be retrained for classification of
new types of data. These properties are likely to he useful for chromosome classification.
Specimen preparation techniques in routine use evolve very rapidly, resulting in changes
in chromosome appearance. In particular, there is an increasing clinical requirement to
use higher-resolution handing for diagnostic purposes, resulting in routine examination of
longer (prometaphase) chromosomes. This will result in the need for greater adaptability in
automated karyotyping systems.
In this paper we present a preliminary investigation into the feasibility of using neural
networks as chromosome classifiers, using the density profile as the representation of the
handing pattern. We compare two commonly used network configurations and assess their
suitability for this problem. The data used for this study are a set of 2904 profiles
from G-handed chromosomes from Rigshospitalet, Copenhagen (Gerdes and Lundsteen
1981). each annotated with the chromosome’s length, centromere position and classification
Neural networks for chromosome classifcafion
961
assigned by an experienced cytogeneticist. The profiles were carehlly measured by
densitometry from photographic negatives, care being taken to avoid overlapped or badly
bent chromosomes. For this reason many of the cells in this data set are incomplete (there
are, on average, 38.2 chromosomes per cell) which does not present a problem for this
study as we are interested solely in classification of isolated chromosomes. However, the
sex chromosomes, particularly the Y chromosomes, are represented by a very small number
of examples. For this reason we have omitted the Y chromosomes from the study, only
using data from the remaining 23 classes.
2. Neural nets
There is a variety of different network architectures, each with its appropriate training
algorithm (see, e.g. Wasserman 1989, or the review in Physics in Medicine and Biology
by Clark (1991)). Two types of network have been predominantly used for classification
problems: the Kohonen self-organizing feature map or Kohonen net (Kohonen 1990) and
the multi-layer perceptron (hl~~).These nets accept continuous-valued rather than binary
inputs and have been shown to generate low classification error rates in a range of other
application domains (Kohonen 1988, Bisset et al 1989).
output layer
(2-0 array of nodes)
hidden layer
input layer
(0)
Figure 2. Neural nenvork architectures. (a)The Kohonen self-organizing feature map. Each
input is connected by a weighted link to each of the nodes in a two-dimensional anay of outputs.
(b) The MLP. The nodes are arranged in layers. Each node in a given layer is connected by
weighted links to each node in the succeeding layer. The example shows a network with n input
nodes, W output nodes and a single hidden layer, as used in this study.
Figure Z(a) shows the topology of a Kohonen net. All input nodes have links to all nodes
in the two-dimensional array of outputs. Associated with each link is a weight, initially
assigned a random value. The value of an output node is the sum of the weighted inputs
on each link and these output values are manipulated by a competitive leaming algorithm
to arrive at an unsupervised clustering of output nodes (Kohonen 1990). As each training
pattern is presented at the input, the output node whose pattern of weights most closely
matches the input pattern is selected as the winner in the competition; its weights, and those
of its neighbours, are updated to be closer to the input pattern, making it more likely to
be selected and updated when a similar pattern is presented. In this way after a number of
presentations of a representative set of training patterns, the output nodes form a map of
regions each of which respond to different patterns in the training set. These regions can be
962
A M Jennings and J Graham
labelled according to the true class of the patterns to which they respond. The learning is
unsupervised since the correct classifications of the input pattern a e not used in adjusting
the net parameters, merely in labelling the clusters after training.
The MLP topology is illustrated in figure 2(b). Nodes are connected in layers, all the
nodes in each layer being connected via weighted links to all nodes in the succeeding layer.
Each node performs a non-linear transformation of the sum of its inputs, and the output
of this transformation is sent along all of the node’s links to the next layer. As it passes
along each link, this value is multiplied by the weight on that link before becoming one of
the inputs to the next node. Each node may have an additional input, in the form of a bias
or threshold which ensures that the summed inputs lie within an appropriate range for the
transforming function. The input pattern is fed into the input layer, passing through several
transformations before generating a pattern of outputs. There may be either one or two
hidden layers of nodes between the inputs and the outputs, which act as feature detectors.
In the experiments which we report below, only one hidden layer is used. For a given
input, the output pattern is determined by the pattern of weights on the links. This pattern
of weights is obtained by supervised training; each input pattern on training generates an
output which is compared with the correct output pattern for its class, and the weights are
adjusted so that the observed output is closer to the desired output. The bias values are also
adjusted as part of the same process. The most commonly used algorithm for adjusting the
weights is error back propagation (Rumelhart et a1 1986). The error signal at the output is
used to propagate adjustments to the weights back through the network so that the resulting
pattern of weights produces outputs closer to those appropriate for the input pattern.
3. The classification experiments
The classification experiments involved training each network with approximately half
of the chromosome data and using the remainder as ‘unseen’ data to test the network‘s
classification performance, reversing the roles of the training and unseen set and averaging
the classification rates. Several network parameters were varied for each network to
investigate the effect on classification performance. One feature common to the two
networks was the form of the input. We wished to use the banding profile to represent
the banding pattern, i.e. to assign one profile sample to each input node.
Cells are measured at different stages of contraction during metaphase, so that the sum of
the lengths of all the chromosomes in a cell varies considerably. Furthermore, chromosomes
do not contract uniformly along their lengths so that not only do longer chromosomes show
more bands than shorter ones but this increase in banding resolution occurs unevenly along
the chromosome. There is therefore considerable inter-cell variation in the appearance of
chromosomes of the same class. One aspect of this variation is in the number of samples
making up a profile, as these are taken at equal spacings along the centreline, typically at
pixel positions in the metaphase image. This variation can be reduced by normalization
of the sum of the chromosome lengths. In our experiments we use the median cell length
as a normalization measure to compensate for the fact that many of the cells had missing
chromosomes.
To ensure that each input to the network corresponds to a consistent feature in the
profiles, all chromosomes were presented using the same number of profile values. The
number of profile value inputs needed to achieve best classification performance was one of
the parameters investigated for each network. The longest profiles in our data set consisted
of 116 elements. Shorter input vectors were generated by adding consecutive elements
Neural networks for chromosome clars@cation
963
togethe: without averaging, a procedure which retains the total chromosome density in the
profile, to produce profiles 58, 29 and 15 elements long. Additional inputs representing
chromosome length and centromeric index were used in the case of the MLP.
In each experiment the measure of performance was the percentage of alI chromosomes
misclassified in both the training set and the unseen test set. A misclassification in this
case was taken to be the assignment of a chromosome to a class other than that to which
it had been assigned by the cytogeneticist when the data set was collected. The important
misclassification rate is, of course, that for the unseen portion of the data, which provides
information on the network's ability to generalize; it is this value we seek to minimize by
selecting appropriate network parameters.
3.1. Kohonen self-organizing map
3.1.1. Mefhodr. The Kohonen map was investigated using only the banding data as input.
Three experiments were conducted.
(i) The number of input nodes. In this experiment the size of the map was fixed at
81 nodes (a 9 x 9 array). Each network, with 116, 58 and 29 input nodes, respectively,
was trained using 30 examples of each of the 23 classes and tested on 50 unseen examples
noting the classification performance. The number of output nodes was chosen to be similar
to that which had been used successfully in a problem of similar magnitude, in which 96
output nodes were used to recognize 18 phonemes (Kohonen 1988).
(ii) The number of training examples. The selection of 30 examples for training in
experiment (i) was rather arbitrary, and the effect on the selected network of altering the
number of training examples was therefore investigated. Classification performance was
noted using training sets of 10, 20, 30 and 40 chromosomes.
(iii) The size of the output map. Finally the effect on classification performance of the
size of the output map was considered. The size of the output map was varied from 7 x I
to 20 x 20 nodes using eight passes of 40 examples of each chromosome for training.
3.1.2. Results. (i) The number of input nodes. Table 1 shows that the classification error
rate on both training and unseen data is relatively insensitive to the number of inputs used
(i.e. to the resoluton at which the banding profile is presented). As both training time and
labelling time are highly dependent on the number of inputs (and hence the number of
weighted links), there is a clear advantage in the use of shorter input vectors. Experiments
(ii) and (iii) were conducted using 29 input nodes.
Table 1. Variation in the average classification error of a Kohonen net as the number of input
values repnenting the banding pattern is varied. Output map size: 9 x % tmining set: 30
examples of each Chromosome class: test set: 50 examples of each class.
Average classification mor (94)
Number of input
values
Training set (690 chromosomes)
Unseen set (1150 chromosomes)
116
24.0
22.8
37.4
37.0
37.1
58
29
22.4
(ii) The number of training examples. Figure 3 demonstrates the effect of the number of
training examples on the net's ability to classify and to generalize to unseen data. Training
A M Jennings and J Graham
964
passes using different numbers of example chromosomes show that when 40 examples are
used (figure 3(d))not only is best classification performance achieved, but the performance
on unseen data matches that on training data, indicating that the net is 'generalizing', or
responding to general features of the training data, rather than specifically modelling the
training examples.
classification
error
classification
errw
loi(a)
0
0
,
,
,
,
2
4
6
8
6
8
1
10
(6)
0
0
2
4
6
8
10
5040-
(4
0
0
(4
0
2
4
training cycle
0
2
4
6
8
training cycle
F i y r c 3. Training the Kohonen net with different numbers of examples of each class. (U)
10, (b) 20, ( c ) 30, ( d ) 40 examples in the training set. The curVeS show the percentage of
chromosomes incorrectly classified in the training se1 (broken) and the unseen set (full) as the
number of passes of the trainins data is increased. There is a clear improvement in both absolute
classification performance and ability to generalize.
(iii) The size of the output map. The effect on classification of the size of the output
map is shown in table 2. A consistent training regime (eight passes of 40 examples,
following the result of experiment (ii)) was used for each map, and under this regime, best
965
Neural networks for chromosome classification
performance was obtained using an 18 x 18 may of output nodes. As with the smaller
maps, only a few passes of training data were required for the network to settle down to a
fairly stable configuration (figure 3), after which the misclassification rates oscillate as the
number of training passes is increased. The minimum misclassification rate observed with
this configuration occurred after six passes of the training data, giving values of 11.8% on
training data and 16.7% on unseen data.
Table 2. Variation in the average classification error of a Kohonen net with the size of the
output map. Input vector size: 29 values; mining set: 40 examples of each class.
Average classification enor (%)
Size of
output map
7x7
9x9
11 x 11
13 x 13
15 x 15
17 x 17
18 x 18
19 x 19
20 x 20
~
~.
Training set (920 chromosomes)
Unseen set (920 chromosomes)
35.4
26.7
39.5
25.9
23.6
23.3
20.3
20.1
18.9
22.3
20.5
22.6
17.2
15.4
14.2
12.7
14.1
8.9
3.2. Multi-her perceptron
3.2.1. Methods. The MLP net was trained using the back-propagation algorithm of Rumelhart
er a1 (1986), the weights and bias values being updated after every presentation of a training
profile. The back-propagation algorithm provides two parameters, gain (or learning rate) and
momentum, controlling the rate at which weights change in response to error signals. We
wished to investigate the effect on classification of varying the gain and momentum values,
as well as the size of the input vector and the number of hidden nodes. For simplicity we
reshicted our study to the use of a single layer of hidden nodes. As we were not aware
of any similar studies in the literature which might give us reasonable stating values for
OUT experiments (as had been the case with the Kohonen net) we conducted some pilot
experiments, similar to those reported below using chromosomes from groups 1-5 only (the
longest chromosomes). The results of these experiments indicated that the number of inputs
representing the banding pattern could be reduced to 15 without loss of classification ability,
and that 15 hidden nodes were adequate. Experimental determination of appropriate gain
and momentum values gave figures of 0.3 and 0.7 respectively (values which have been
used successfully in other net simulations; see, e.g. Lippmann 1987).
All the nets tested had 23 output nodes, one for each class (Ychromosomes being
omitted). The desired output is therefore close to unity at the output node corresponding to
the correct class, and zero elsewhere. The classification produced by the network on being
presented with a test pattern was taken to be the node with the highest output, even if this
was significantly lower than unity.
(i) Gain and momentum. The gain term q determines the rate at which weights are
altered in response to an observed error signal. A large value of gain (near 1.0) produces
fast training and is useful in moving weights rapidly away from their initial random values.
However, once the weight configuration is close to a minimum in error space, relatively large
weight shifts can have the effect of ‘jumping’out of a global minimum and into a nearby
966
A M Jennings and J Graham
local minimum. Small values of gain are more appropriate later in training and a useful
approach is to successively reduce the learning rate as training proceeds. Two measures of
network performance may be used to determine the points at which the gain term is reduced.
These are the total net error (the sum of the absolute values of the differences between the
desired and observed net outputs over a txaining pass) and the classification performance
on training data. Both of these measures reflect the net’s classification ability, but they
are not identical, due to the fact that only the output node with the highest value affects
classification. At different stages of the learning process one may be more useful than the
other. This difference between these two measures has been noted in other applications
(Dah1 1987). The weight change at a node at a given training cycle, determined by the
observed error signal and the gain, may be further augmented by a fraction of the weight
change which occurred at the previous cycle. In this way successive weight changes in the
same direction are encouraged, whereas weight changes in successively different directions
are damped, reducing oscillatory behaviour. The momentum term 01 specifies the fraction of
the previous weight change which is added at each cycle. We investigated the best choices
for momentum and initial gain, as well as the effect of reducing gain using the two criteria
described above.
(ii) The number of input nodes. The result of our pilot experiment, that the profiles
could be reduced to 15 samples (one eighth of the length of the longest profile), was tested
by measuring classification performance on all 23 classes using a network with 15 hidden
nodes, using gain and momentum values determined in experiment (i).
(iii) The number of hidden nodes. The classification performance was determined using
different numbers of nodes in the hidden layer.
(iv) The use of additional chromosome features. Experiments (i)-(iii) were designed
to examine the feasibility of configuring an MLP to use the density profile as a banding
representation for classification. As noted in the introduction, chromosome size and
centromere position are also important classification features. To test the overall
classification performance of our network, two additional input nodes were included for
the normalized length and the centromeric index. me centromere divides the chromosome
into a long ‘arm’ and a short ‘arm’ (figure l(b)). The centromeric index is the ratio of the
length of the short arm to the whole chromosome length.) The effect on classification of
adding these features was examined.
Results. (i) Gain and momentum. The effect of reducing gain during training is
demonstrated in figure 4, which shows a succession of training passes for a 15-15-23
network. Each training cycle involved the presentation of 1150 chromosomes. Figure 4(u)
compares the network convergence on training with and without a reduction in gain. In this
case gain was halved whenever a 10% increase in net error occurred or if the total number
of correctly classified chromosomes had not increased by at least two over the previous
presentation of the training data. The gain reduction method clearly results in improved
convergence. Figure 4(b) demonstrates the effectiveness of using both tota1 net error and
classification performance as criteria for reducing gain. The starting value of gain was
0.3 and momentum was 0.7, as determined by the pilot study. Figure 5(a) and (b) shows
training passes using different values of momentum and initial gain confirming that 0.7 and
0.3 are the most appropriate for this configuration.
(ii) The number of input nodes. Table 3 confirms that the classification performance is
fairly insensitive to the number of values used to represent the banding profile (and hence,
the numbers of inputs). No loss in classification accuracy is observed when an input vector
of 15 values is used.
3.2.2.
Neural networks for chromosome clussi&ution
961
classification
error
..-
x
- no reduction in gain term
10
(4
0
0
2
4
8
6
10
12
14
16
18
20
."
Gain term reduced using
A
- net error only
+ - net error and Classification performance
40
30
..
. . . . . . . . . . . . . . . . . . . . . . . . .
0
8
1 6 ' 2 4 3 2 4 0 4 8 5 6 6 4 7 2 8 0 8 8
training cycle
Figure 4. The effect of reducing gain during vaining of the MW.A 15-15-23 net was
used with momentum (I = 0.7 and initial value of gain q = 0.3. The graphs show the
percentage of the training set incorrectly classified as the data are successively presented to
the network.. (a)Comparison of no gain reduction with gain reduction based on totll network
enor. (b) Comparison of gain reduction criteria. Total network error alone compared with
network emx and classification performance combined.
(iii) The number of hidden nodes. The choice of 15 nodes in the single hidden layer is
confirmed by figure 5(c) which shows training passes of 15-10-23.15-15-23 and 15-20-23
networb.
A M Jennings and J Graham
968
classiocation
emor
classification
error
M
b
4
8
I6
12
20
24
(4
0
0
4
8
I2
20
16
training cycle
0
4
8
12
16
20
24
Figure 5. The effect on MLP training of varying
networlt parameters The percentage of the training
set incorrectly classified is shown as training proceeds.
( 6 ) Varying the value of the momenluin term (I. The
gain term q is initially set to 0.3 in each case and
reduced during mining as described in the text. x. a =
0.9; A, a = 0.7 and +, (I = O S . (b)Varying the starring
value of the gain term 4. The momentum term (I is set
to 0.7 in each case. x. q = 0.5: A, 4 = 0.3 and +.
q = 0.1. (c) Varying the number of nodes in the hidden
layer. = 0.7, q = 0.3. x, 10 nodes; A, 15 nodes and
+, 20 nodes.
Table 3. Variation in classification e m r rate of the MLP with the number of input vdues. The
network had 15 hidden nodes and 23 output nodes.
Number of inout
values
15
58
116
Avenge classification error (%)
,
,
Training set (1150 chromosomes)
U n y n set (690 chromosomes)
2.2
3.9
3.0
10.1
10.0
10.3
(iv) The use of additional chromosome features. Table 4 shows the effect on
classification rates of using additional inputs for normalized chromosome length and
centromeric index using (16 or 17)-15-23 networks. These features clearly contribute
siznificantly to classification performance. The overall best misclassification rates observed
were 2.6% on training data and 6.6% on unseen data.
Table 4. The contributions of chromosome features to classification by the M W
Features used for
cIassiR ctltion
Grey level profile
Grey level profile and normalized length
Grey level profile, normalized length
and ana centromeric index
Average classifiuIion error (5%)
.
, , ,
Training set (990 chromosomes)
Unseen set (990 chromosomcs)
4.3
4.0
10.9
8.8
2.6
6.6
Neural networks for chromosome classij'ication
969
4. Discussion
This preliminary study has investigated the feasibility of using neural network classifiers as
part of an automated chromosome analysis system. The motivation for investigating neural
networks in this application is their potential adaptability to changes in the data arising
from evoluton in the sample preparation techniques and the desire to use a classifier making
use of a more natural representation of the banding pattern than has been used in previous
studies.
The MLP shows considerablepromise as a classifier. By varying the operating parameters
we have found a configuration which is capable of achieving useful classification rates. Our
search of the parameter space was not broad and, even within its own narrow limits, not
exhaustive. The final configuration of parmeters may not therefore be the best obtainable,
but it is gratifying to note that a 'good' combination was found fairly rapidly. It will be
the subject of further study to investigate whether a more thorough search of parameter
space will improve the network further. For comparison, the best published classification
rates to be found in the literature (to our knowledge) are those reported by Piper and
Granum (1989) who achieve 5.9% misclassifications on a superset of the profile data used
here. The additiond data used by these authors included a number of badly bent and some
overlapping chromosomes (excluded from our data). Their results, however, include the
effect of a further classification step which imposes the constraint that each chromosome
class contains at most two chromosomes. While our results are not directly comparable
with theirs, we are encouraged to achieve similar classification performance on similar data.
Our experiments with the MLP demonstrate that considerable advantage is to be gained by
careful adjustment of network parameters and mining conditions.
Table 5. Comparison of the results obtained for chromosome classification using a Kohonen
net with parameters and results for two other studies. The classification accuracy reported for
phoneme recognition including post-processing using a context-sensitive grammar.
Number of inputs
Output map size
Number of classes
Number of training examples
Error for unseen set (%)
Recognition of
phonemes
Chromosome
classification
Recognitition of the spoken words
'yes' and 'no'
29
18 x 18
23
40
16.7
15
15
7x7
2
798
8x12
6.9
3-8
18
50
It is unsurprising that the performance of the Kohonen map is inferior to the MLP in this
application. For one thing, supervised training is much more appropriate to this data than
unsupervised training. Table 5 shows a comparison of our results with two other applications
of the Kohonen map on phoneme recognition (Kohonen 1988) and on recognition of the
spoken words 'yes' and 'no' (Lucas and Kittler 1989). The results on phoneme recognition
include a final supervised training phase, and refer to the classification accuracy of speech
after processing the neural net output using a context-sensitive grammar (similar in its effect
to the rearrrangment included in the results of Piper and Granum). It is tempting to speculate
that better classification results could be obtained using the Kohonen map for chromosome
classification, for example by increasing the size of the training set. This option was not
available to us in this study, and the more promising performance of the MLP suggests that
development of that route is more appropriate as a practical approach to this problem.
970
A M Jennings and J Graham
Acknowledgments
This work was supported by funding from the Science and Engineering Research Council.
It was greatly facilitated by the exchange of materials within the Concerted Action of
Automated Cytogenetics Groups, supported by the European Community (project II.1.1113).
References
Bisset D L, Filho E and Fairhunt M C 1989 A comparative study of neural network stmcNres for practical
application in a pattern recognition environment Is1 IEE Int C o d on Arlificiul Neural Networks (London,
19891 (London:
pp 37&82
Clark J W 1991 Neural network modelling Phvs. Med B i d . 36 1259-317
Dah1 D E 1987 Accelerated learning usingthegeneralised delta mle lE&E I s l l n l . Can$ on Neural Neworkr vol2
(New York: IEEE)pp 523-30
Gerdes T and Lundsteen C 1981 Documenlalion elhe Rigshmpilal Chromosome Densiry Profile Dura Base
Department of Obstetrics and Gynaecology YA and Department of Paediatrics, RigshospitaleL University
of Copenhagen
Graham J 1987 Automation of routine c l i n i d chromosome analysis I. Karyotyping by machine Anal. Quonr.
Cylol. Hisfol. 9 383-90
Graham J and Piper J 1993 Automatic karyotype analysis Chromasome Analysis ProMcols ed I R Gosden (Cliffon,
NI: Humana) at press
Graham J and Fycock D 1987 Automation of routine clinical chromosome analysis 11. metaphase finding Anal.
Quonr. Cytol. H i d . 9 391-7
Gmlund G H 1976 Identification of human chromosomes using.integrated
density ~rofilesIEEE Truu, Biomed.
.
Eng. BME-23 183-92
G m u m E 1982 Amlicakion of statistical and syntactical methods of analysis to classification of chromosome data
Pallern Reeo&irion TheorynndApplicot& ed J Kirtler. K S Fu and L F Pan NATO AS1 (Dordrecht: Reidel)
pp 373-98
Groen F C A, tenKate T K,Smeulders A W M and Young I T 1989 Human chromosome classification based on
local band descriptors Panem Recognition lelt 9 21 1-22
Havkin S and Dens! C 1991 Classification of radar clutter usinn
- neural networks IEEE Trans.Neural Networks
"-2589600
Kohonen T 1988 The neural phonetic typewriter Compurer 21 11-22
- 1990 Se~Orgmtsmonid Arsocralive Memory.3rd edn (Bcrlm: Springer)
Lippmmnn R P 1987 An introduction 10 computing with neunl ne& /€&E ASSP Mag. 4 h??
Luws A E and Kittler J I989 A compmtive study of the Kohonen and multiedit neuml net I m g dgorithm
Irr IEE Inr Conf on Anificiol .Seeural Vcnvorkr ( L o n d m 19891 (London: LEE) pp 7-1 I
Lundsrecn C. Gxdcs T. G m u m E and PNlip J 1981 Aaom3lic ehromosomc analysis n. Kllryoryping of banded
human chromosomes using band lnnsition sequences Ciin. Genu. 19 2 6 3 6
Lundsteen C, Lind A-M and Cmnum E 1976 Ksud classitcanon of banded human chromosomes 1. Kqoryping
mmpxcd with classification of isolxcd chromosomes Am. 1. Hum Genei. 40 81-97
Lundsteen C and h l m n A 0 1989 On the selection of systems lor nutomarcd cylogenetic mdysis A n 1. Med.
Gener. 32 72-80
hpcr J 3nd G m u m E 1989 On fully aulomatic measuiemcnt for banded chromosome classification Cyiomerry 10
242-85
Rumelhart D E. Hinton G E and Willims R J 1986 Leaming mternd rcprecenwuons by m o r propagation Parollel
Dislribured Pmcerringr Erpiorortom in !he Microrrrueiurerof Cognilion YOI
I , Foundztions sd D E Rumclhart
and J L McCellmd (Cambridge. MA. MlT press) pp 51842
Sejnosski T J and Rosenburg C R 1987 Parallel networks that I- to pronounce Engllsh text ComplexSyre,ns
111848
Thomason .U G m d G m u m E 1986 Dynmically prognmmcd inrexnce or hlxkov networks from finire sets or
sample swing IEEE Tmm. P..MI P&\n-8 491-801
\h'~ssermanP 1949 .Veurol C o m p i i n g - T k q ond Prmiice (New York. Yon Noswand Reinhold)
i~m
~~
.